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Friday, 23 March 2012

Refraction of Waves

(Updated on 2/10/2013: to include latest SPM (2012) questions)

1. Refraction occurs when waves change direction as they enter one medium from another at an obligue angle. If a wave moves from one medium into another at right angle, there is no refraction because there is no change in direction of the wave.

2. Refraction happens because a wave moves at different speeds in different media - faster in less dense medium (or deeper water) and slower in denser medium (or shallow water).

3. The frequency of a wave in different media does not change. It is the change in wavelength that causes the wave speed to change.

     (For the above reason (24/2/2015): When a single-colour (or monochromatic) light gets refracted when it moves from one optical medium into another at an oblique angle, its wavelength changes but NOT its colour nor frequency. Hence, a monochromatic light is best described as either a single-colour light or a single-frequency light and NOT as a single-wavelength light because the wavelength can change while the colour and the frequency remain the same!)

4.  Since wave speed v = λf: when waves move from a less dense medium (or deeper water) to denser medium (or shallower water), wavelength decreases resulting in decrease in wave speed (frequency unchanged); and, conversely,  when waves move from a denser medium (or shallower water) to a less dense medium (or deeper water), wavelength increases causing the wave speed to increase. .

[Decrease in wavelength λ means successive wavefronts get closer; and, conversely, increase in wavelength (and thus wave speed) means the wavefronts get further apart]

5. When the angle of incident i of a wave as it enters another medium is zero (i.e. the direction of travel of wave is parallel to the normal or at right angle to the interface between the 2 media), there is no change in direction of the wave and therefore no refraction occurs. However, the wavelength and thus the wave speed change (since frequency remains unchanged) as its move from one medium into another medium.

6. Refraction occurs IF the angle of incident i` of the waves as they enter another medium is > zero,
   that is,  i` > 0o:
  • waves direction bends towards normal if the waves move from a less dense medium (or deeper water) to denser medium (or shallower water);
  • waves direction bends away from normal if the waves move from a denser medium (or shallower water) to a less dense medium (or deeper water).

(SPM 2012 P1 Q35 @ pg 340 on characteristics of water waves undergoing refraction)

 6. Refraction of Light obeys Snell's Law: Sin i` / sin r` = n, the refractive index. (i = angle in air or vacuum, and r = angle in the other medium whichever direction the waves travel)
  • Other formulae for Refractive Index n (Form 4 Chapter 5 on "Light"):
    • n = sin 90` / sin c` = 1 / sin c` (where c = critical angle for total internal reflection). Note: Critical angle c and total internal reflection are always in the denser medium;
    • n = Speed of Light in vacuum (or in air approximately) / Speed of Light in the medium;
    • n = Real Depth (Vertical) / Apparent Depth

7. Natural Phenomena of Refraction: 
  • Water waves: Sea wavefronts tend to take the shape of the shoreline as they approach the shore. Explanation: 
  • In the centre of the ocean, the wavefronts are straight and parallel to each other because the water waves there travel at uniform speed as the depth of sea water there is almost uniform. 
  • When the wavefronts approach the shoreline, they reach the headland or cape earlier than the bay because the cape represents the protruding part of the shoreline that becomes shallow earlier than the bay.
  • Therefore, the water waves near the headland or cape slow down first - thus, their wavelength becomes smaller or wavefronts become closer near the cape while those approaching the bay are still having greater wavelength and their wavefronts are still further apart
  • This phenomenon of refraction of water waves causes the wavefronts to take the shape of the shoreline as the waves approach the shore.

                         Refraction of Water Waves

  • Water wave refraction causes wavefronts to be parallel to the shape of the coastline as they approach the shore.
  • Water wave refraction also causes water wave energy to converge at cape and causing erosion - the waves at the cape are more rocky and turbulent.
  • Water wave energy diverges at bay and spreads out to a wider region, causing deposition of sand, etc. The amplitude of waves at the bay is smaller than at the cape. The waves at the bay are calmer. It is safer to swim in water near the bay than near the cape. 

  • Sound Waves:
  • During a hot day - sound can be heard only a short distance away unlike on a cool night because:
  • during daytime, air near the surface of the earth is warmer and less dense;
  • while higher up, air is cooler and denser. 
  • Sound is therefore refracted upwards progressively towards the normal and away from the surface of the earth:

  • During a cool night - the opposite effect happens:
  • Sound can be heard a longer horizontal distance away because 
  • air is cooler and denser near the earth surface than higher up - 
  • sound is refracted upwards progressively away from the normal until it is reflected back to the earth surface. (SPM 2010 P2 Q10(b) at pg. 260)
  • (SPM 2012 P2 Q10(b) at pg 361)
  • Light Waves:
    • Pool or tub looks shallower
    • Submerged part of spoon, drinking straw or ruler looks bent
    • Pencil or ruler appears broken when viewed through a glass block
    • Atmospheric refraction of rising or setting sun:
      • the Sun below the horizon appears above horizon;
      • the Sun looks oval and flattened
    • Atmospheric refraction of the stars:
      • the twinkling effect
      • the star appears higher than its actual position
    • Divers' or fish's 96o cone-view of the abovewater world and 42o  view of the underwater world (assuming critical angle of the sea water being 48o)

(Points for discussion: Please refer Malaysian Form 5 KBSM Physics textbook:
  • At pg. 36: "Refraction of waves is a phenomenon where there is a change of direction in the propagation of waves when they move from one medium to another due to a change of speed." However, a change in wave speed such when the wave enters another medium at right angle (or zero angle of incidence) does not necessarily mean a change in wave direction i.e. does not necessarily result in refraction!
  • At pg 13, the 2nd paragraph on refraction: "By comparing the angle of incidence, i with angle of refraction, r in Figure 1.19, you will find that when waves travel from a denser medium to a less dense medium, they are refracted towards the normal." Shouldn't the words "towards the normal" be "away from normal"? Very serious fundamental error!
  • On the above textbook error at page 13: On 10/9/2013, I tried calling the telephone number given inside the front-cover of book but found it no longer in use. So, I wrote an email to the Ministry of Education. Here are my email and the Ministry's reply. The Ministry agrees with my findings and will be taking follow-up remedial actions:


To: Whom It May Concern (; 03-8884 5027)

From: A Concerned Parent

Re: Significant Errors in Malaysian Form 5 Physics and Chemistry Textbooks (KBSM)

In good faith, I write to inform about what I think are significant errors in the above-mentioned Form 5 Science stream textbooks.

If the Ministry agrees that they are indeed serious errors, I sincerely hope that "Corrections Circulars" can be sent out urgently to notify all relevant parties - particularly the Form 5 Science students who will be sitting for their SPM exams. very soon. The errors:

1. Form 5 Physics Textbook (KBSM):
  • At page 13: the 2nd paragraph on refraction: "By comparing the angle of incidence, i with angle of refraction, r in Figure 1.19, you will find that when waves travel from a denser medium to a less dense medium, they are refracted towards the normal." The correct underlined wordings should be "away from normal" and not "towards the normal" . This is a very serious fundamental error!

2. Form 5 Chemistry Textbook (KBSM):
  • At page 188: The chemical formula for "lauryl alcohol" was given twice there as CH3(CH2)9CH2OH. The correct chemical formula for "lauryl alcohol" should be: CH3(CH2)10CH2OH (error highlighted in red).
I would be grateful for your follow-up actions.

Thank you.

Douglas Tan
(Handphone: 011-xxxx xxxx)

The reply from the Ministry of Education was prompt (within just 8 days) and professional: The Ministry agrees with me that there is basis to my statement that they are significant errors and that it will expeditiously carry-out follow-up actions on the errors ("Correction Circulars" to all schools throughout the country that are using the textbooks, I believe).

The Ministry's reply on 18/9/2013:
Ramlan Abu Talib <>
8:51 AM (6 hours ago)
to mePengarahParidinCheKrishnanSyedSimWan

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En. Douglas Tan,


1.     Saya dengan hormatnya merujuk kepada e-mel tuan kepada Bahagian Buku Teks, Kementerian Pendidikan Malaysia,  bertarikh 10 September 2013 berhubung perkara di atas.

2.     Penyataan tuan terhadap kesilapan fakta dalam buku teks Physics Form 5 dan Chemistry Porm 5 KBSM telah dirujuk kepada Sektor Penerbitan Sekolah Menengah untuk penelitian.

3.     Setelah dibuat penelitian , pihak kami mendapati bahawa penyataan pihak tuan terhadap hal ini mempunyai asas.

4.     Pihak kami akan melaksanakan tindakan penambahbaikan dan tindakan susulan terhadap hal ini dengan segera.

5.     Pihak kami mengucapkan terima kasih di atas keprihatinan dan kerjasama tuan terhadap hal ini.

Sekian, terima kasih.

Ramlan bin Haji Abu Talib
b.p Pengarah
Ketua Unit Khidmat Selia
Sektor Penyeliaan dan Penyelidikan
Bahagian Buku Teks, Kementerian Pelajaran Malaysia
Aras 1-3, Blok E-15, Parcel E
(03-88844484) ) (019-6644435) (Fax-03-88844489)

  • Posted and updated on 13/1/2015 by:

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Thank you.


1 comment:

Rohan Rao said...

I was struggling with waves in class, this page was very helpful, thanks so much, now I can show my friends this site because they are struggling too :P